Find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ [on hold]$(y_n)$ bounded sequence and $limfrac(x_n)(y_n)=0$ show $lim(x_n) = 0$Find the limit of the sequence with $n$th term $x_n = left(frac2n+3n^2right)^n$Convergence and upper bound of $sum_n fracsinleft[left(pi-frac14right)(x_n-x_m)right]x_n-x_msinleft(fracx_n+x_m4right)$.If $x_nto 0$ and $y_n=fracx_1-x_2-…-x_nn$ then $y_nto 0$Find $limlimits_n to infty fracx_nn$ when $limlimits_n to infty x_n+k-x_n$ existsProve that the sequence $z_n$, where $z_n:= x_n-y_n$, converges and $lim (x_n-y_n)=lim z_n = (lim x_n) - (lim y_n)$sequence $x_n+1=x_n+e^-2018x_n$Asymptotics of the sequence defined by $x_n+1 = x_n + frac2x_n$, $x_0=1$Limit of the infinite sequence involving $a_n, s_n$Concluding whether $(y_n)_n$ is a bounded sequence
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Find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ [on hold]
$(y_n)$ bounded sequence and $limfrac(x_n)(y_n)=0$ show $lim(x_n) = 0$Find the limit of the sequence with $n$th term $x_n = left(frac2n+3n^2right)^n$Convergence and upper bound of $sum_n fracsinleft[left(pi-frac14right)(x_n-x_m)right]x_n-x_msinleft(fracx_n+x_m4right)$.If $x_nto 0$ and $y_n=fracx_1-x_2-…-x_nn$ then $y_nto 0$Find $limlimits_n to infty fracx_nn$ when $limlimits_n to infty x_n+k-x_n$ existsProve that the sequence $z_n$, where $z_n:= x_n-y_n$, converges and $lim (x_n-y_n)=lim z_n = (lim x_n) - (lim y_n)$sequence $x_n+1=x_n+e^-2018x_n$Asymptotics of the sequence defined by $x_n+1 = x_n + frac2x_n$, $x_0=1$Limit of the infinite sequence involving $a_n, s_n$Concluding whether $(y_n)_n$ is a bounded sequence
$begingroup$
If $x_n$ is the solution in the interval $left(n pi, n pi + fracpi2right)$ of the equation $ tanx=x$, where $n$ is a natural number, find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ when $n$ goes to $infty$. I tried to apply Cesaro Stolz or Taylor series but doesn't work. Can you give me some hints?
sequences-and-series
edited yesterday
rtybase
11.4k31533
asked yesterday
rafarafa
618212
$endgroup$
put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 2 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel
add a comment |
$begingroup$
If $x_n$ is the solution in the interval $left(n pi, n pi + fracpi2right)$ of the equation $ tanx=x$, where $n$ is a natural number, find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ when $n$ goes to $infty$. I tried to apply Cesaro Stolz or Taylor series but doesn't work. Can you give me some hints?
sequences-and-series
edited yesterday
rtybase
11.4k31533
asked yesterday
rafarafa
618212
$endgroup$
put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 2 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday
add a comment |
$begingroup$
If $x_n$ is the solution in the interval $left(n pi, n pi + fracpi2right)$ of the equation $ tanx=x$, where $n$ is a natural number, find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ when $n$ goes to $infty$. I tried to apply Cesaro Stolz or Taylor series but doesn't work. Can you give me some hints?
sequences-and-series
edited yesterday
rtybase
11.4k31533
asked yesterday
rafarafa
618212
$endgroup$
If $x_n$ is the solution in the interval $left(n pi, n pi + fracpi2right)$ of the equation $ tanx=x$, where $n$ is a natural number, find the limit of the sequence $y_n = nleft(npi + fracpi2 - x_nright)$ when $n$ goes to $infty$. I tried to apply Cesaro Stolz or Taylor series but doesn't work. Can you give me some hints?
sequences-and-series
sequences-and-series
edited yesterday
rtybase
11.4k31533
asked yesterday
rafarafa
618212
edited yesterday
rtybase
11.4k31533
asked yesterday
rafarafa
618212
edited yesterday
rtybase
11.4k31533
edited yesterday
rtybase
11.4k31533
edited yesterday
rtybase
11.4k31533
11.4k31533
asked yesterday
rafarafa
618212
asked yesterday
rafarafa
618212
asked yesterday
rafarafa
618212
618212
put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 2 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel
put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 2 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday
add a comment |
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday
add a comment |
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1fgBW i75,0es 469j7D,es,gG,2r2JbucG hL,xf4lTayAu,eVM
$begingroup$
The $n$th root of $tan x = x$ is $x_n = pi n + pi/2 - epsilon$, and you need $tan x_n$ to approximately match $pi n$. From this you can find $epsilon$ to the first order. Incidentally, $x_n$ is the $n$th positive zero of the Bessel function $J_3/2(x)$.
$endgroup$
– Maxim
yesterday